Localization Transition in a Ballistic Quantum Wire

TL;DR

This paper investigates the transition from extended to localized many-body electron states in a one-dimensional quantum wire as electron density decreases, revealing a sharp transition with Coulomb blockade signatures.

Contribution

It provides experimental evidence of a localization transition in a 1D quantum wire and introduces a theoretical model for the observed states at low electron numbers.

Findings

Abrupt transition from extended to localized states at critical density

Observation of Coulomb blockade features with discrete tunneling resonances

Double-lobed momentum distributions in few-electron states

Abstract

The many-body wave-function of an interacting one-dimensional electron system is probed, focusing on the low-density, strong interaction regime. The properties of the wave-function are determined using tunneling between two long, clean, parallel quantum wires in a GaAs/AlGaAs heterostructure, allowing for gate-controlled electron density. As electron density is lowered to a critical value the many-body state abruptly changes from an extended state with a well-defined momentum to a localized state with a wide range of momentum components. The signature of the localized states appears as discrete tunneling features at resonant gate-voltages, corresponding to the depletion of single electrons and showing Coulomb-blockade behavior. Typically 5-10 such features appear, where the one-electron state has a single-lobed momentum distribution, and the few-electron states have double-lobed distributions with peaks at $\pm k_F$. A theoretical model suggests that for a small number of particles (N<6), the observed state is a mixture of ground and thermally excited spin states.